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1. CMB 2013 (vol 57 pp. 188)

Rad, Nader Jafari; Jafari, Sayyed Heidar
A Characterization of Bipartite Zero-divisor Graphs
In this paper we obtain a characterization for all bipartite zero-divisor graphs of commutative rings $R$ with $1$, such that $R$ is finite or $|Nil(R)|\neq2$.

Keywords:zero-divisor graph, bipartite graph
Categories:13AXX, 05C25

2. CMB 2011 (vol 56 pp. 407)

Rad, Nader Jafari; Jafari, Sayyed Heidar; Mojdeh, Doost Ali
On Domination in Zero-Divisor Graphs
We first determine the domination number for the zero-divisor graph of the product of two commutative rings with $1$. We then calculate the domination number for the zero-divisor graph of any commutative artinian ring. Finally, we extend some of the results to non-commutative rings in which an element is a left zero-divisor if and only if it is a right zero-divisor.

Keywords:zero-divisor graph, domination
Categories:13AXX, 05C69

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